The sci-fi drama - an "edgier, scarier" spinoff from the UK original - debuts tonight at 9pm on Watch.
Niall Matter - who plays series lead Evan Cross - told DS that having an established fanbase for the new Primeval was a "blessing" and a "testament to the original".
"We have to live up to certain expectations, and I believe that we do that and more with New World," said the former Eureka actor.
His co-star Sara Canning (Dylan Weir) added: "We're hoping to appeal to the original fanbase, grab some new fans along the way and just build on what the original series was."
> Primeval: New World has 'harder edge', says star Niall Matter
Connor Temple - played in the original series by Andrew-Lee Potts - also appears on New World and acts as something of a mentor and guide to Evan Cross.
"The character of Connor Temple was my favourite from the original Primeval so having him join us was a real pleasure," Matter revealed.
Danny Rahim, who plays firearms expert Mac Rendell, hinted: "Who's to say who else could come into our world? Anybody really... from the [original show]."